Stockpile Inventory Modernization Act of 2020 This bill authorizes the Department of Health and Human Services (HHS) to transfer certain supplies from the Strategic National Stockpile to any federal department or agency on a reimbursable basis, provided that (1) the supplies are less than six months from their expiration date, (2) the stockpile is able to replenish them, and (3) the transfer is in the best interest of the government. HHS shall submit a report to Congress that includes each transfer and the amount reimbursed for the supplies. The authority to make such transfers terminates on September 20, 2023.